Question

If the complement of an angle is one fifth its supplement find the measure of the angle

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{angle}\mathrm{be}\mathrm{x}. \\ \mathrm{Complement}\mathrm{of}\mathrm{the}\mathrm{angle}=90°-\mathrm{x} \\ \mathrm{Supplement}\mathrm{of}\mathrm{the}\mathrm{angle}=180°-\mathrm{x} \\ \mathrm{Given},\mathrm{Complement}\mathrm{of}\mathrm{the}\mathrm{angle}=\frac{1}{5}\left(\mathrm{Supplement}\mathrm{of}\mathrm{the}\mathrm{angle}\right) \\ \Rightarrow 90°-\mathrm{x}=\frac{1}{5}\left(180°-\mathrm{x}\right) \\ \Rightarrow 450°-5\mathrm{x}=180°-\mathrm{x} \\ \Rightarrow 270°=4\mathrm{x} \\ \Rightarrow \mathrm{x}=67.5° \end{gathered}$$
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